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Parallelograms

Parallelograms. Definitions. Quadrilateral- polygon with 4 sides Parallelogram- quadrilateral with both pairs of opposite sides parallel Opposite sides- do not share a vertex Opposite angles- do not share a side. Theorem 6-3. Opposite sides of a parallelogram are congruent. Theorem 6-4.

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Parallelograms

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  1. Parallelograms

  2. Definitions • Quadrilateral- polygon with 4 sides • Parallelogram- quadrilateral with both pairs of opposite sides parallel • Opposite sides- do not share a vertex • Opposite angles- do not share a side

  3. Theorem 6-3 • Opposite sides of a parallelogram are congruent.

  4. Theorem 6-4 • Consecutive angles of a parallelogram are supplementary • Why is this true? What kinds of angles are these (think about parallel lines cut by a transversal)?

  5. Theorem 6-5 • Opposite angles of a parallelogram are congruent.

  6. Theorem 6-6 • Diagonals of a parallelogram bisect each other.

  7. Problem 3 (p.362) • Given: • KP=y+10 • MP=2x-8 • LP=x • NP=y+2 • Find x and y. • Find KM and LN. • y=14, x = 16, KM=48, LM=32

  8. Theorem 6-7 • If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  9. Complete the following questions about the diagram below. • If RS= 12, then ST= ______? • If AB= 8, then BC= ______? • If AC= 20, then AB= ______? • If AC= 10x, then BC=______? A R B S C T

  10. Problem • Find x and y. • x=1.5; y=7 • Find DF and CA • DF=10, CA=12

  11. Answer True or False(Remember, for a statement to be true, it must be true ALL of the time!) 1. Every parallelogram is a quadrilateral. True 2. Every quadrilateral is a parallelogram. False 3. All the angles of a parallelogram are congruent. False 4. All sides of a parallelogram are congruent. False 5. In RSTU, RS || TU. True 6. In ABCD, if m<A=50, then m<C=130. False

  12. Homework • p.364 #9-12 all, 14, 15, 17-27 odd, 31, 38, and 39

  13. Proofs with Parallelograms • p. 364 #13, p.365#32-37

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